Looks like a lot of my recs have been covered in other comments, but for sci fi by a woman I've got to recommend Lois McMaster Bujold! The Vorkosigan Saga is one of my favourite series, and also contains several of my favourite books :)
(I am not much of a Katara person--I mean, no, I like her a lot, I just don't feel very driven to read fic about her, if that makes sense. But my sister, who's a huge Zutarian, very much is, and has repeatedly expressed disappointment over Katara's characterization in fic. I asked her if she had any recs where "Katara is in character, interesting, and Doing It for Herself"/for fic like such selfish prayers. She said Forty Weeks wasn't bad? I can't second the recommendation, not having read it myself, but I thought I'd at least pass it along.)
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(I am not much of a Katara person--I mean, no, I like her a lot, I just don't feel very driven to read fic about her, if that makes sense. But my sister, who's a huge Zutarian, very much is, and has repeatedly expressed disappointment over Katara's characterization in fic. I asked her if she had any recs where "Katara is in character, interesting, and Doing It for Herself"/for fic like such selfish prayers. She said Forty Weeks wasn't bad? I can't second the recommendation, not having read it myself, but I thought I'd at least pass it along.)